Input/loss method for determining boiler efficiency of a fossil-fired system

ABSTRACT

The operation of a fossil-fueled thermal system is quantified by obtaining an unusually accurate boiler efficiency. Such a boiler efficiency is dependent on the calorimetric temperature at which the fuel&#39;s heating value is determined. This dependency affects the major thermodynamic terms comprising boiler efficiency.

This application claims the benefit of U.S. Provisional Application No.60/147,717 filed Aug. 6, 1999, the disclosure of which is herebyincorporated herein by reference.

This invention relates to a fossil-fired boiler, and, more particularly,to a method for determining its thermal efficiency to a high accuracyfrom its basic operating parameters.

CROSS REFERENCES

This application is related to U.S. Pat. Nos. 5,367,470 and 5,790,420which patents are incorporated herein by reference in their entirely.Performance Test Codes 4.1 and 4 published by the American Society ofMechanical Engineers (ASME) are incorporated herein by reference intheir entirely.

BACKGROUND OF THE INVENTION

The importance of accurately determining boiler efficiency is criticalto any thermal system which heats a fluid by combustion of a fossilfuel. If practical day-to-day improvements in thermal efficiency are tobe made, and/or problems in thermally degraded equipment are to be foundand corrected, then accuracy in efficiency is a necessity.

The importance of accurately determining boiler efficiency is alsocritical to the Input/Loss Method. The Input/Loss Method is a patentedprocess which allows for complete thermal understanding of a steamgenerator through explicit determinations of fuel and effluent flows,fuel chemistry including ash, fuel heating value and thermal efficiency.Fuel and effluent flows are not directly measured. The Method isdesigned for on-line monitoring, and hence continuous improvement ofsystem heat rate.

The tracking of the efficiency of any thermal system, from a classicalindustrial view-point, lies in measuring its useful thermal output,BBTC, and the inflow of fuel energy, m_(AF)(HHVP+HBC). m_(AF) is themass flow of fuel, HHVP is the fuel's heating value, and HBC is theFiring Correction term. For example, the useful output from afossil-fired steam generator is its production of steam energy flow.Boiler efficiency (η_(B-HHV)) is given by:η_(B-HHV)=BBTC/[m_(AF)(HHVP+HBC)]. The measuring of the useful output ofthermal systems is highly developed and involves the directdetermination of useful thermal energy flow. Determining thermal energyflow generally involves measurement of the inlet and outlet pressures,temperatures and/or qualities of the fluids being heated, as well asmeasurement of the fluid's mass flow rates (m_(stm)). From thisinformation specific enthalpies (h) may be determined, and thus thetotal thermal energy flow, BBTC=Σm_(stm)(h_(outlet)−h_(inlet)),delivered from the combustion gases may be determined.

However, when evaluating the total inflow of fuel energy, problemsfrequently arise when measuring the flow rate (m_(AF)) of a bulk fuelsuch as coal. Further, the energy content of coal, its heating value(HHV), is often not known with sufficient accuracy. When suchdifficulties arise, it is common practice to evaluate boiler efficiencybased on thermal losses per unit mass flow of As-Fired fuel (i.e.,Btu/lbm_(AF)); where: η_(B-HHV)=1.0−(ΣLosses/m_(AF))/(HHVP+HBC). Forevaluating the individual terms comprising boiler efficiency, such asthe specific loss term (ΣLosses/m_(AF)), there are available numerousmethods developed over the past 100 years. One of the most encompassingis offered by the American Society of Mechanical Engineers (ASME),published in their Performance Test Codes (PTC).

INTRODUCTION TO NEW APPROACH

This invention teaches the determination of boiler efficiency havingenhanced accuracy. Boiler efficiency, if thermodynamically accurate,will guarantee consistent system mass/energy balances. From suchconsistencies, fuel flow and effluent flow then may be determined,having greater accuracy than prior art, and greater accuracy thanobtained from direct measurements of these flows.

Before discussing details of the present invention it is useful toexamine ASME's PTC 4.1, Steam Generating Units, and PTC 4, Fired SteamGenerators. Both PTC study a boiler efficiency based on the higherheating value (η_(B-HHV)), no mention is made of a lower heating valuebased efficiency (η_(B-LHV)). Using PTC 4.1's Heat-Loss Method, higherheating value efficiency is defined by the following. For Eq. (1A), HHV,if determined from a constant volume bomb calorimeter, is corrected fora constant pressure process, termed HHVP. Gaseous fuel heating values,normally determined assuming a constant pressure process, need no suchcorrection, HHVP=HHV. $\begin{matrix}{\eta_{B - {HHV}} = \frac{{HHVP} + {HBC} - {\sum{{Losses}/m_{AF}}}}{{HHVP} + {HBC}}} & \text{(1A)}\end{matrix}$

Using PTC 4's Heat-Balance Method, higher heating value efficiency isdefined as: $\begin{matrix}{\eta_{B - {{HHV}/{fuel}}} = \frac{{HHVP} - {\sum{{Losses}/m_{AF}}}}{HHVP}} & \text{(1B)}\end{matrix}$

The above are considered indirect means of determining boilerefficiency. Eq. (1A) implies that the input energy in fuel & FiringCorrection m_(AF)(HHVP+HBC) less ΣLosses, describes the “Energy FlowDelivered” from the thermal system, the term BBTC. The newer PTC 4(1998, but first released in 2000) advocates only the use of heatingvalue in the denominator, developing a so-called “fuel” efficiency,η_(B-HHV/fuel). It is important to recognize that once efficiency isdetermined using an indirect means, fuel flow may be back-calculatedusing the classic definition provided BBTC is determinable:m_(AF)=BBTC/[η_(B-HHV)(HHVP+HBC)]; or m_(AF)=BBTC/[η_(B-HHV/fuel)HHVP].

The concept of the Enthalpies of Products and Reactants is nowintroduced as important to this invention. These terms both defineheating value and justify the Firing Correction term (HBC) as beingintrinsically required in Eq. (1A) Higher heating value is the amount ofenergy released given complete, or “ideal”, combustion at a defined“calorimetric temperature”. For a solid fuel such as coal, evaluated ina constant volume bomb, the combustion process typically heats a waterjacket about, and is corrected to, the calorimetric temperature. Anysuch ideal combustion process is the difference between the enthalpy ofideal products (HPR_(Ideal)) less reactants (HRX_(Cal)) both evaluatedat the calorimetric temperature, T_(Cal). Correction from a constantvolume process (HHV) associated with a bomb calorimeter, if applicable,to a constant pressure process (HHVP) associated with the As-Firedcondition is made with the ΔH_(V/P) term, see Eq. (37B).

δQ_(T-Cal) =−HHV=−HHVP+ΔH _(V/P)  (2A)

HHVP≡=−HPR _(Ideal) +HRX _(Cal)  (2B)

This invention teaches that only when fuel is actually fired at exactlyT_(Cal), and whose combustion products are cooled to exactly T_(Cal), isthe thermodynamic definition of heating value strictly conserved. At anyother firing and cooling temperatures, Firing Correction and sensibleheat losses must be applied. At any other temperature the so-called“fuel” efficiency (which ignores the HBC correction), isthermodynamically inconsistent. At any other temperature, evaluation ofthe HRX_(Cal) term must be corrected to the actual As-Fired conditionthrough a Firing Correction referenced to T_(Cal). The HPR_(Ideal) termis corrected to the actual via loss terms referenced to T_(Cal) whereappropriate (that is, anywhere a Δenergy term is applicable).

When a fossil fuel is fired at a temperature other than T_(Cal), theFiring Correction term HBC must be added to each side of Eq. (2B):

HHVP+HBC=−HPR _(Ideal) +HRX _(Cal) +HBC  (3A)

Eq. (3A) implies that for any As-Fired condition, the systems' thermalefficiency is unity, provided the HPR_(Ideal) term is conserved (i.e.,system losses are zero, and ideal products being produced at T_(Cal)).For an actual combustion process, the HPR_(Ideal) term of Eq. (3A) isthen corrected for system losses, forming the basis of boilerefficiency:

η_(B-HHV)(HHVP+HBC)=−HPR _(Ideal)−ΣLosses/m _(AF) +HRX _(Cal) +HBC  (3B)

This invention recognizes that the HPR_(Ideal) term of Eqs. (2B) & (3A),and thus Eq. (3B), is key in accurately computing boiler efficiencystemming from Eq. (3B). This invention teaches that all terms comprisingEq. (3B) must be evaluated with methodology consistent with a boiler'senergy flows, but also, and most importantly, in such a manner as to notimpair the numerical consistency of the HPR_(Ideal) term as referencedto T_(Cal).

The approaches contained in prior art have not appreciated using theconcept of T_(Cal), used for thermodynamic reference of energy levels asaffecting the major terms comprising boiler efficiency. It is believedthat prior approaches evaluated fuel heating value, and especially thatof coal, only to classify fuels. Boiler efficiencies were determined asrelative quantities. Accuracy in heating value, and in the resultantcomputed fuel flow, was not required but only accuracy in the totalsystem fuel inflow of energy was desired. The accuracy needed in boilerefficiency by the Input/Loss Method, given that fuel chemistry, fuelheating value and fuel flow are all computed, requires the method ofthis invention. Further, commercial needs for high accuracy boilerefficiency was not required until recent deregulation of the electricpower industry which has now necessitated improved accuracy.

The sign convention associated with the HPR & HRX terms of Eq. (2B)follows the assumed convention of a positive numerical heating value,thus the non-conventional sense of HPR & HRX. In some technicalliterature the senses of HPR & HRX terms may be found reversed forsimplicity of presentation. An example of typical values includes:[−HPR_(Act-HHV)+HRX_(Act-HHV)]=−(−7664)+(−1064), Btu/lbm. The sign ofsensible heat terms, ∫dh, follows thisdifference:−HPR_(Act)−∫dh_(Products); and +HRX_(Act)+∫dh_(Reactants).Heats of Formation, ΔH_(f) ⁰, are always negative quantities. From Eq.(3B), higher heating value boiler efficiency is then given by:$\begin{matrix}{\eta_{B - {HHV}} = \frac{{- {HPR}_{Ideal}} - {\sum{{Losses}/m_{AF}}} + {HRX}_{Cal} + {HBC}}{{HHVP} + {HBC}}} & \text{(3C)}\end{matrix}$

For certain fuels the PTC procedures are flawed by not recognizing thecalorimetric temperature, T_(Cal), and its impact on the HPR_(Ideal)term. As discussed below, for certain coals having high fuel water, andfor gaseous fuels, use of the calorimetric temperature becomes mandatedif using the methods of this invention for accurate boiler efficiencies;without such consideration, errors will occur. There is no mention ofthe calorimetric temperature in PTC 4.1 nor in PTC 4. PTC 4.1 referencesenergy flows to an arbitrary “reference air temperature”, T_(RA). PTC 4references energy flows to a constant 77.0F. PTC 4.1 nor 4 mention howthe reference temperature should be evaluated. U.S. Pat. No. 5,790,420(bottom of col.18) also assumes a constant reference temperature at77.0F, without mention of a variable calorimetric temperature, nor howthe reference temperature should be evaluated. There is no mention of acalorimetric temperature as used in boiler efficiency calculations inthe technical literature. Further, the PTC 4 procedure is flawed byrecommending a so-called “fuel” efficiency, which, again, is indisagreement with the base definition of heating value if the fuel isactually fired (As-Fired) at a temperature other than T_(Cal). For somehigh energy coals the effects of ignoring T_(Cal) have minor impact.However, when using coals having high water contents (e.g., lignitescommonly found in eastern Europe and Asia), and for gaseous fuels, sucheffects may become very important.

To illustrate, consider a simple system firing pure carbon in dry air,having losses only of dry gas, effluent CO and unburned carbon. AssumeForced Draft (FD) and Induced Draft (ID) fans are used having W_(FD) &W_(ID) energy flows. Applying PTC 4.1 §7.3.2.02, but using nomenclatureherein, dry gas loss is evaluated at the reference air temperature, thusL_(G′) in Btu/lbm_(AF) is given by:

L _(G′) =C _(P/Gas)(T _(Stack) −T _(RA))M′ _(Gas)  (4)

Incomplete combustion is described (§7.3.2.07) as the fraction of COproduced relative to total possible effluent CO₂ times the difference inHeats of Combustion of carbon and CO.

L _(CO)=(−ΔH _(f-Cal/CO2) ⁰ +ΔH _(f-Cal/CO) ⁰)M′ _(CO)  (5)

Unburned carbon is described in PTC 4.1 §7.3.2.07, as the flow of refusecarbon times its Heat of Combustion:

L _(UC)=(−ΔH _(f-Cal/CO2) ⁰)M′ _(C/Fly)  (6)

For this simple example, and assuming unity fuel flow, the so-called“boiler credits” as defined, in part, by PTC 4.1 are determined as:

HBC′=C _(P/Fuel)(T _(Fuel) −T _(RA))+C _(P/Air)(T _(Amb) −T _(RA))M′_(Air) +W _(FD)  (7)

In these equations the M′_(i) weight fractions are relative to As-Firedfuel, and have direct translation to 4.1 usage. PTC 4.1 efficiency isthen given by the following, after combining the above quantities intoEq. (3C), and re-arranging terms: $\begin{matrix}{\eta_{B} = \frac{\begin{matrix}{{- {HPR}_{Ideal}} - {{C_{P/{Gas}}\left( {T_{Stack} - T_{RA}} \right)}M_{Gas}^{\prime}} - W_{ID} -} \\{{\left( {{{- \Delta}\quad H_{f - {{Cal}/{CO2}}}^{0}} + {\Delta \quad H_{f - {{Cal}/{CO}}}^{0}}} \right)M_{CO}^{\prime}} -} \\{{\left( {{- \Delta}\quad H_{f - {{Cal}/{CO2}}}^{0}} \right)M_{C/{Fly}}^{\prime}} + {HRX}_{Cal} + {C_{P/{Fuel}}\left( {T_{Fuel} - T_{RA}} \right)} +} \\{{{C_{P/{Air}}\left( {T_{Amb} - T_{RA}} \right)}M_{Air}^{\prime}} + W_{FD}}\end{matrix}}{{HHVP} + {HBC}}} & (8)\end{matrix}$

The present invention is a complete departure from all known approachesin determining boiler efficiency, including PTC 4.1 and PTC 4. Eq. (8)illustrates the generic approach followed by PTC 4.1 and PTC 4, whichhas been used by the power industry for many years. However, thisinvention recognizes and corrects several discrepancies which affectaccuracy. These discrepancies include the following items.

1) The enthalpy terms HPR_(Ideal) & HRX_(Cal) as referenced to thecalibration temperature, when “corrected” to system boundary conditionsusing (T_(Stack)−T_(RA)) & (T_(Fuel)−T_(RA)) is wrong sinceT_(RA)≠T_(Cal). Although the effects on HPR_(Ideal) from HBC referencedto T_(RA), may cancel; the effects on HPR_(Ideal) from theΣLosses/m_(AF) term, as referenced to T_(RA), does not cancel. See PTC4.1 §7.2.8.3 & §7.3.2.02.

2) PTC 4.1 addresses unburned fuel and incomplete combustion throughHeats of Combustion. Although numerically correct as referenced toHPR_(Ideal), a more logical approach is to describe actualproducts—their effluent concentrations and specific Heats of Formation,ΔH_(f-Cal) ⁰. For example, although the above M′_(Gas). is descriptiveof actual combustion products, differences between actual and idealdemand numerical consistency with HHVP, product formations andassociated heat capacities. See PTC 4.1 §7.3.2.01, −07.

3) Uncertainty is present when using Heats of Combustion associated withunburned fuel. As coal pyrolysis creates numerous chemical forms (thebreakage of aliphatic C—C bonds, elimination of heterocycle complexes,the hydrogenation of phenols to aromatics, etc.), the assumption of anencompassing ΔH_(C) ⁰ used by PTC 4.1 is optimistic. For example,various graphites have a wide variety of ΔH_(C) ⁰ values (from 13,970 to14,540 Btu/lb depending on manufacturing processes). An improvedapproach is use of consistent Heats of Formation coupled with measuredeffluent gas concentrations and balanced stoichiometrics.

4) HHVP reflects formation of ideal combustion products at T_(Cal);water thus formed must be referenced to ΔH_(f-Cal/liq) ⁰ and h_(f-Cal)(not illustrated above). For example, if using T_(RA) as reference,water's ΔH_(f/liq) ⁰ varies from −6836.85 Btu/lbm at 40F to −6811.48Btu/lbm at 100F, h_(f) from 8.02 to 68.05 Btu/lbm. Holding these termsconstant is suggested by PTC 4.1 §7.3.2.04.

5) PTC 4.1 §7.3.2.13 pulverizer rejected fuel losses are described bythe rejects weight fraction times rejects heating value, HHV_(Rej) (notillustrated above). This is correct only if the heating value is thesame as the As-Fired. If mineral matter is concentrated in the rejects(reflected by a HHV_(Rej) term), then fuel chemistry (and HPR & HRXterms) must be adjusted, again, to conserve HPR_(Ideal) for theAs-Fired.

Of course, one could equate T_(RA) to T_(Cal) (not suggested by PTC 4.1or 4), and solve some of the problems. However, the rearrangement ofindividual terms of Eq. (8) and then, most importantly, theircombinations into HPR_(Act), HRX_(Act) and HBC terms evaluated atT_(Cal), provides the nucleus for this invention. These methods are notemployed by any known procedure. First, the issue of possibleinconsistency between ideal arid actual products is addressed bysimplifying (for the example cited) the entire numerator of Eq. (8) to[−HPR_(Act)+HRX_(Act)]. In this, the Enthalpy of Products, HPR_(Act),encompasses effluent sensible heat and ΔH_(f-Cal) ⁰ terms associatedwith actual products, including all terms associated with incompletecombustion. The Enthalpy of Reactants, HRX_(Act), is defined as[HRX_(Cal)+HBC], the last line of Eq. (8); HRX_(Cal) is evaluated as[HHVP+HPR_(Ideal)] from Eq. (2B). Second, use of the[−HPR_(Act)+HRX_(Act)] concept allows ready introduction of thecalorimetric temperature (or any reference temperature if applicable) asaffecting both ∫dh and ΔH_(f-Cal) ⁰ terms. Third, the[−HPR_(Act)+HRX_(Act)] concept provides generic methodology for anycombustion situation. It is believed the elimination of individual lossterms associated with combustion (cornionly used by the industry and aspracticed in PTC 4.1 and PTC 4) greatly reduces error in determiningtotal stack losses, including the significant dry stack gas loss term aswill be seen; [−HPR_(Act)+HRX_(Act)]=HHVP+HBC−Σ(Stack Losses)/m_(AF).

The use of the term “boiler credit” (for HBC′) as used by the PTCs ismisleading since terms comprising HBC intrinsically correct the fuel'scalorimetric energy base to As-Fired conditions. HBC is herein termedthe “Firing Correction”. HBC is not a convenience nor arbitrary, it isrequired for HHVP consistency and thus valid boiler efficiencies leadingto consistent mass and energy balances.

Although the basic philosophies of PTC 4.1 and 4 are useful and havebeen employed throughout the power industry, including prior Input/LossMethods, they are not thermodynamically consistent. To address theseissues this invention includes establishing an ordered approach toboiler efficiency calculations employing a strict definition of heatingvalue, that is, consistent treatment of the Enthalpy of Products, theEnthaply of Reactants and the Firing Correction such that the numericalevaluation of the HPR_(Ideal) term is conserved.

This invention teaches the determination of lower heating value basedboiler efficiency (commonly used in Europe, Asia, South America andAfrica), such that fuel flow rate is computed the same from either alower or a higher heating value based efficiency.

Other advantages of this invention will become apparent when the detailsof the method of the present invention is considered.

SUMMARY OF INVENTION

This invention teaches the consistent application of the calorimetrictemperature to the major terms comprising determination of boilerefficiency. The preferred method of the application of such atemperature is through the explicit calculation of these major terms,which include the Enthalpy of Products, HPR_(Act), the Enthalpy ofReactants, HRX_(Act), and the enthalpy of Firing Correction, HBC. Thismethod advocates an ordered and systematic approach to the determinationof boiler efficiency. For some fuels, under certain conditions,techniques of this invention may be applied using an arbitrary referencetemperature.

BRIEF DESCRIPTION OF DRAWING

FIG. 1 is a block flow diagram illustrating the approach of theinvention.

DETAILED DESCRIPTION OF INVENTION

Definitions of Equation Terms with Typical Units of Measure:

Molar Ouantities Related to Stoichiometrics

x=Moles of As-fired fuel per 100 moles of dry gas product (the assumedsolution “base”).

a=Molar fraction of combustion O₂, moles/base.

n_(i)=Molar quantity of substance i, moles/base.

N_(j)=Molecular weight of compound j.

α_(k)=As-Fired (wet-base) fuel constituent per mole of fuel Σα_(k)=1.0;k=0, 1, 2, . . . 10.

b_(A)=Moisture in entering combustion air, moles/base.

βb_(A)=Moisture entering with air leakage, mole/base.

b_(Z)=Water/steam in-leakage from working fluid, moles/base.

b_(PLS)=Molar fraction of Pure LimeStone (CaCO₃) required for zero CaOproduction, moles/base.

γ=Molar ratio of excess CaCO₃ to stoichiometric CaCO₃ (e.g., γ=0.0 if noeffluent CaO).

z=Moles of H₂O per effluent CaSO₄, based on lab tests.

σ=Kronecker function: unity if (α₆+α₉)>0.0, zero if no sulfur is presentin the fuel.

β=Air pre-heater dilution factor, a ratio of air leakage to truecombustion air, molar ratio.

β=(R_(Act)−1.0)/[aR_(Act)(1.0+φ_(Act))]

R_(Act)=Ratio of total moles of dry gas from the combustion processbefore entering the air pre-heater to gas leaving; defined as the airpre-heater leakage factor.

φ_(Act)=Ratio of non-oxygen gases (nitrogen and argon) to oxygen in thecombustion air, molar ratio.

φ_(Act)≡(1.0−A_(Act))/A_(Act)

A_(Act)=Concentration of O₂ in the combustion air local to (andentering) the system, molar ratio.

Ouantities Related to System Terms

BBTC=Energy Flow Delivered derived directly from the combined combustionprocess and those energy flows which immediately effect the combustionprocess, Btu/hr.

C_(P-i)=Heat capacity for a specific substance i, Btu/lb−ΔF.

HBC≡Firing Correction, Btu/lbm_(AF).

HBC′≡Boiler Credits defined in ASME PTC 4.1, Btu/lbm_(AF).

ΔH_(f-77) ⁰=Heat of Formation at 77.0 F, Btu/lbm or Btu/lb-mole

ΔH_(f-Cal) ⁰=Heat of Formation at T_(Cal), Btu/lbm or Btu/lb-mole.

HHV=Measured or calculated higher heating value, also termed the grosscalorific value, Btu/lbm_(AF).

HHVP=As-Fired (wet-base) higher heating value, based on HHV, correctedfor constant pressure process, Btu/lbm_(AF).

HNSL≡Non-Chemistry & Sensible Heat Losses, Btu/lbm_(AF).

HPR≡Enthalpy of Products from combustion (HHV- or LHV-based),Btu/lbm_(AF).

HRX≡Enthalpy of Reactants (HHV- or LHV-based), Btu/lbm_(AF).

HR=System heat rate, Btu/kWh.

HSL≡Stack Losses (HHV- or LHV-based), Btu/lbm_(AF).

L_(i)=Specific heat loss term for a ith process, Btu/lbm_(AF).

LHV=Lower heating value based on measurement, calculation or based onthe measured or calculated higher heating value, LHV is also termed thenet calorific value, Btu/lbm_(AF).

LHVP=As-Fired (wet-base) lower heating value, based on LHV, correctedfor a constant pressure process, Btu/lbm_(AF).

M′_(i)=Weight fraction of ith effluent or combustion air relative toAs-Fired fuel, —.

m_(AF)≡As-Fired fuel mass flow rate (wet with ash), lbm_(AF)/hr.

Q_(SAH)=Energy flow delivered to steam/air heaters, Btu/hr.

P_(Amb)≡Ambient pressure local to the system, psiA.

T_(Amb)≡Ambient temperature local to the system, F.

T_(Cal)≡Calorimetric temperature to which heating value is referenced,F.

T_(AF)=As-Fired fuel temperature, F.

T_(RA)≡Reference air temperature to which sensible heat losses andcredits are compared (defined by PTC 4.1), F.

T_(Slack)≡Boundary temperature of the system effluents, commonly takenas the “stack” temperature, F.

W_(FD)=Brake power associated with inflow stream fans (e.g., ForcedDraft fans) within the system boundary, Btu/hr.

W_(ID)=Brake power associated with outflow stream fans (e.g., InducedDraft & gas recirculation fans), Btu/hr.

WF_(k)=Weight fraction of component k, —.

η_(B)=Boiler efficiency (HHV- or LHV-based), —.

η_(C)=Combustion efficiency (HHV- or LHV-based), —.

η_(A)=Boiler absorption efficiency, —.

Introduction to Boiler Efficiency

The preferred embodiment for determining boiler efficiency, η_(B),divides its definition into two components, a combustion efficiency andboiler absorption efficiency. This was done such that an explicitcalculation of the major terms, as solely impacting combustionefficiency, could be formulated. This invention teaches the separationof stack losses (treated by terms effecting combustion efficiency), fromnon-stack losses (treated by terms effecting boiler absorptionefficiency).

η_(B)=η_(C)η_(A)  (9)

To develop the combustion efficiency term, the Input/Loss Method employsan energy balance uniquely about the flue gas stream (i.e., thecombustion process). This balance is based on the difference in enthalpybetween actual products HPR_(Act), and actual reactants HRX_(Act).Actual, As-Fired, Enthalpy of Reactants is defined in terms of FiringCorrection: HRX_(Act)≡HRX_(Cal)+HBC. Combustion efficiency is defined byterms which are independent of fuel flow. Its terms are integrallyconnected with the combustion equation, Eq. (19) discussed below.$\begin{matrix}{\eta_{C - {HHV}} \equiv \frac{{- {HPR}_{Act}} + {HRX}_{Act}}{{HHVP} + {HBC}}} & (10)\end{matrix}$

This formulation was developed to maximize accuracy. Typically forcoal-fired units, typically over 90% of the boiler efficiency'snumerical value is comprised of η_(C). All individual terms comprisingη_(C) have the potential of being determined with high accuracy.HPR_(Act) is determined knowing effluent temperature, completestoichiometric balances, and accurate combustion gas, air and waterthermodynamic properties. RRX_(Act) is dependent on HPR_(Ideal), heatingvalue and the Firing Correction. HBC applies the needed corrections forthe reactant's sensible heat: fuel, combustion air, limestone (or othersorbent injected into the combustion process), water in-leakage andenergy inflows . . . all referenced to T_(Cal) (detailed below).

The boiler absorption efficiency is developed from the boiler's“non-chemistry & sensible heat loss” term, HNSL, i.e., product sensibleheat of non-combustion processes associated with system outflows. It isdefined such that it, through iterative techniques, may be computedindependent of fuel flow: $\begin{matrix}{\eta_{A} \equiv {1.0 - \frac{HNSL}{{- {HPR}_{Act}} + {HRX}_{Act}}}} & (11) \\{{~~~~}{= {1.0 - \frac{HNSL}{\eta_{C - {HHV}}\left( {{HHVP} + {HBC}} \right)}}}} & (12)\end{matrix}$

HNSL comprises radiation & convection losses, pulverizer rejected fuellosses (or fuel preparation processes), and sensible heats in: bottomash, fly ash, effluent dust and effluent products of limestone (or othersorbent). HNSL is determined using a portion of PTC 4.1's Heat-LossMethod.

The definition of η_(A) allows η_(B) of Eq. (3C) to be evaluated usingHPR_(Act) & HRX_(Act) terms, illustrating consistency with Eq. (1A),explained as follows. Since: HSL≡HPR_(Act)−HPR_(Ideal);[−HPR_(Act)+HRX_(Act)]=HHVP+HBC−HSL; the following is evident:$\begin{matrix}{\eta_{B - {HHV}} \equiv \quad {\left\lbrack \frac{{- {HPR}_{Act}} + {HRX}_{Act}}{{HHVP} + {HBC}} \right\rbrack \left\lbrack \frac{{- {HPR}_{Act}} + {HRX}_{Act} - {HNSL}}{{- {HPR}_{Act}} + {HRX}_{Act}} \right\rbrack}} & {~~~} & {\quad \text{(13A)}} \\{= \quad \frac{{- {HPR}_{Act}} + {HRX}_{Act} - {HNSL}}{{HHVP} + {HBC}}} & ~ & {\quad \text{(13B)}} \\{= \quad \frac{{HHVP} + {HBC} - {HSL} - {HNSL}}{{HHVP} + {HBC}}} & ~ & {\quad \text{(13C)}} \\{= \quad {1.0 - \frac{\Sigma \quad {Losses}}{m_{AF}\left( {{HHVP} + {HBC}} \right)}}} & ~ & {\quad \text{(13D)}} \\{= \quad \frac{BBTC}{m_{AF}\left( {{HHVP} + {HBC}} \right)}} & ~ & {\quad \text{(13E)}}\end{matrix}$

where ΣLosses≡m_(AF)(HSL+HNSL). The Energy Flow Delivered from thecombustion process, BBTC, is m_(AF)(HHVP+HBC) less ΣLosses.

Equating Eqs. (13B) and (13E) results in defining the specific EnergyFlow Delivered, BBTC/m_(AF). Since HNSL and BBTC are the same for eitherHHV- or LHV-based calculations, the enthalpy difference[−HPR_(Act)+HRX_(Act)] must be identical.

−HPR _(Act−HHV) +HRX _(Act−HHV) ≡−HPR _(Act−LHV) +HRX _(Act−LHV)  (14)

With a computed boiler efficiency, the As-Fired fuel flow rate, m_(AF),may be back-calculated: $\begin{matrix}{m_{AF} = \frac{BBTC}{\eta_{B - {HHV}}\left( {{HHVP} + {HBC}} \right)}} & (15)\end{matrix}$

Assuming T_(Cal) is not known and an arbitrary thermodynamic referencetemperature (T_(RA)) must be used, T_(Cal)=T_(RA), then the practicalityof any boiler efficiency method should be demonstrated through thesensitivity of the denominator of Eq. (15) with its assumed referencetemperature. Fuel flow, BBTC, and HHVP are constants for a given systemevaluation. In regards to fuel flow, the use of an arbitrary T_(RA) iscompatible with the methods of this invention provided the computed fuelflow of Eq. (15) is demonstrably insensitive to a “reasonable change” inthe thermodynamic reference temperature, T_(RA). By “reasonable change”in the thermodynamic reference temperature is meant the likely range ofthe actual calorimetric temperature. For solid fuels this likely rangeis from 68F to 95F, or as otherwise would actually be used in practicingbomb calorimeters. For gaseous fuels, whose heating values are computed,not measured, this likely range is whatever would limit the variation incomputed fuel flow to less than 0.10%. This invention teaches that theproduct η_(B−HHV)(HHVP+HBC) be demonstrably constant for any reasonablerange of T_(RA), if used. This is not to suggest that effects on η_(B)and HR may be ignored if fuel flow is found insensitive; theinsensitivity of η_(B) and HR must be demonstrated through theHPR_(Ideal) term, before a given T_(RA) is justified. However, if η_(B)is mis-evaluated through mis-application of T_(RA), effects on fuel floware not proportional given the influence of the HBC term evaluated usingthe methods of this invention. A 1% change in η_(B) (e.g., 85% to 84%)caused by a change in T_(RA) will typically produce a 0.2% to 0.4%change (Δm_(AF)/m_(AF)) in fuel flow, which is considered notacceptable. Further, Eq. (15) also illustrates that the use of a fuelefficiency (in which HBC≡0.0), in combination with an arbitraryreference temperature is flawed: since η_(B)=f(T_(RA)), and BBTC & HHVPare constants, changes in computed fuel flow are then proportional toη_(B), and wrong.

Once fuel flow is correctly determined, stoichiometric balances are thenused to resolve all boiler inlet and outlet mass flows, includingeffluent flows required for regulatory reporting. The computation ofeffluent flow is taught in U.S. Pat. No. 5,790,420, col.22, line 38 thrucol.23, line 17; but without the benefit of high accuracy fuel flow astaught by this invention. System heat rate associated with asteam/electric power plant follows from Eq. (15) in the usual manner.The effects on HR given mis-application of T_(RA) will compound (add)the erroneous effects from η_(B) and fuel flow. $\begin{matrix}{{{HR}_{HHV} \equiv \quad {{m_{AF}\left( {{HHVP} + {HBC}} \right)}/{Power}}}\quad} & {\quad (16)} \\{= \quad {{BBTC}/\left( {\eta_{B - {HHV}}\quad {Power}} \right)}} & {\quad (17)}\end{matrix}$

Given the commercial importance of computing fuel & emission flows forindustrial systems, and determining system heat rate consistent withthese flows, accurately determining boiler efficiency is important (uponwhich these quantities are based). The determination of on-line fuelheating values, coupled to sophisticated error analysis as used by theInput/Loss Method, demands integration of stoichiometrics with highaccuracy boiler efficiency.

Foundation Principles and Nomenclature

To assist in understanding, discussed is the determination of Heats ofFormation evaluated at T_(Cal). By international convention,standardized Heats of Formation are referenced to 77F (25C) and 1.00 barpressure. For typical fossil combustion, pressure corrections arejustifiably ignored. To convert to any temperature from 77F thefollowing approach is used: $\begin{matrix}{{\Delta \quad H_{f - T}^{0}} = {{\Delta \quad H_{f - 77}^{0}} + {\int_{77}^{T}\quad {h_{Compound}}} - {\sum{\int_{77}^{T}\quad {h_{Elements}}}}}} & (18)\end{matrix}$

Use of the 77F-base standard is important as it allows consistency withpublished values. Consistent ΔH_(f-T) ⁰ values for CO₂, SO₂ and H₂Oallow consistent evaluations of the HPR_(Ideal) term, and the differencebetween the As-Fired heating value plus Firing Correction and[−HPR_(Act)+HRX_(Act)] . . . thus intrinsically accounting for stacklosses and the vagaries of coal pyrolysis given unburned fuel. Thefinest compilation of Heats of Formulation and other properties is theso-called CODATA work (Cox, Wagman, & Medvedev, CODATA Key Values forThermodynamics, Hemisphere Publishing Corp., New York, 1989). Enthalpyintegrals used in Eq. (18) and elsewhere herein are obtained from thework of Passert & Danner (Industrial Eninee Chemistry, Process Desin andDeveloment, Volume 11, No. 4, 1972; also see Manual for PredictingChemical Process Design Data, Chapter 5, AIChE, N.Y., 1983, revised1986). All fluid components in the thermal system (e.g., combustiongases, water in the combustion effluent, moist combustion air, gaseousconstituents of air) must use a consistent dead state for thermodynamicproperty evaluations. Preferred methods employ 32.018F as a uniform deadstate temperature, T_(Dead), and 0.08872 psiA pressure, for allproperties (e.g., the defined zero enthalpy for dry air, gaseouscompounds, saturated liquid water, etc.). Thermodynamic properties areevaluated in the usual manner, for example from T_(Dead) to T_(Cal), andfrom T_(Dead) to T_(Stack), thus net the evaluation from T_(Cal) toT_(Stack).

Given such foundations, Eq. (18) with CODATA, Heats of Combustion ofgaseous fuels, given their known chemistries, may be computed for anycalorimetric temperature (e.g., at the industrial standard of 60F &14.73 psia; see ASTM D1071 & GPA 2145). Solid and liquid fuel heatingvalues, determined by test using an adiabatic or isoperibol bombcalorimeter, are in theory referenced to 68.0F (20C). Refer to ASTMD271, D1989, D2015 & D3286 for coals (being replaced by D5865), and ASTMD240 for liquid fuels. The 68F reference for solid fuels is rarelypracticed; typically, coal bombs are typically conducted at 82.5F or95F. Knowing the calorimetric temperature, if using this temperature instrict compliance with the definition of heating value, all systemenergies affecting boiler efficiency may then be computed.

The following combustion equation is presented for assistance inunderstanding nomenclature used in the detailing procedures. Refer toU.S. Pat. No. 5,790,420 for additional details. The nomenclature used isunique in that brackets are included for clarity. For example, theexpression “α₂[H₂O]” means the fuel moles of water, algebraically α₂.The quantities comprising the combustion equation are based on 100 molesof dry gaseous product. $\begin{matrix}{{{x\left\lbrack {{\alpha_{0}\left\lbrack {C_{YR}H_{ZR}} \right\rbrack} + {\alpha_{1}\left\lbrack N_{2} \right\rbrack} + {\alpha_{2}\left\lbrack {H_{2}O} \right\rbrack} + {\alpha_{3}\left\lbrack O_{2} \right\rbrack} + {\alpha_{4}\lbrack C\rbrack} + {\alpha_{5}\left\lbrack H_{2} \right\rbrack} + {\alpha_{6}\lbrack S\rbrack} + {\alpha_{7}\left\lbrack {CO}_{2} \right\rbrack} + {\alpha_{8}\lbrack{CO}\rbrack} + {\alpha_{9}\left\lbrack {H_{2}S} \right\rbrack} + {\alpha_{10}\lbrack{ash}\rbrack}} \right\rbrack}_{{As}\text{-}{Fired}\quad {Fuel}} + {b_{Z}\left\lbrack {H_{2}O} \right\rbrack}_{{In}\text{-}{Leakage}} + \left\lbrack {\left( {1 + \beta} \right)\left( {{a\left\lbrack O_{2} \right\rbrack} + {a\quad {\varphi_{Act}\left\lbrack N_{2} \right\rbrack}} + {b_{A}\left\lbrack {H_{2}O} \right\rbrack}} \right)} \right\rbrack_{Air} + \left\lbrack {\left( {1 - \gamma} \right){b_{PLS}\left\lbrack {CaCO}_{3} \right\rbrack}} \right\rbrack_{{As}\text{-}{Fired}\quad {PLS}}} = {{d_{Act}\left\lbrack {CO}_{2} \right\rbrack} + {g_{Act}\left\lbrack O_{2} \right\rbrack} + {h\left\lbrack N_{2} \right\rbrack} + {j_{Act}\left\lbrack {H_{2}O} \right\rbrack} + {k_{Act}\left\lbrack {SO}_{2} \right\rbrack} + \left\lbrack {{e_{Act}\lbrack{CO}\rbrack} + {f\left\lbrack H_{2} \right\rbrack} + {l\left\lbrack {SO}_{3} \right\rbrack} + {m\lbrack{NO}\rbrack} + {p\left\lbrack {N_{2}O} \right\rbrack} + {q\left\lbrack {NO}_{2} \right\rbrack} + {t\left\lbrack {C_{YP1}H_{ZP1}} \right\rbrack} + {u\left\lbrack {C_{YP2}H_{ZP2}} \right\rbrack}} \right\rbrack_{{Minor}\quad {Components}} + {x\quad {\alpha_{10}\lbrack{ash}\rbrack}} + {\sigma \quad {b_{PLS}\left\lbrack {{{CaSO}_{4} \cdot z}\quad H_{2}O} \right\rbrack}} + \left\lbrack {\left( {1 - \sigma + \gamma} \right){b_{PLS}\lbrack{CaO}\rbrack}} \right\rbrack_{{Excess}\quad {PLS}} + {v\left\lbrack C_{Refuse} \right\rbrack} + \left\lbrack {\beta \left( {{a\left\lbrack O_{2} \right\rbrack} + {a\quad {\varphi_{Act}\left\lbrack N_{2} \right\rbrack}} + {b_{A}\left\lbrack {H_{2}O} \right\rbrack}} \right)} \right\rbrack_{{Air}\quad {Leakage}}}} & (19)\end{matrix}$

Eq. (19) contains terms which allow consistent study of any combinationof effluent data, especially the principle “actual” effluentmeasurements d_(Act), g_(Act), j_(Act), and the system terms β, φ_(Act)& R_(Act). By this is meant that data on either side of an airpre-heater may be employed, in any mix, with total consistency. Thisallows the stoichiometric base of Eq. (19), of 100 moles of dry gas, tobe conserved at either side of the air pre-heater: dry stack gas=dryboiler=100 moles.

Details of Boiler Efficiency Calculations

The following paragraphs discuss detailed procedures associated with theInput/Loss Method of determining boiler efficiency. The FiringCorrection is closely defined and only relates to terms correctingHRX_(Cal).

Absorption efficiency, η_(A), is based on the non-chemistry & sensibleheat loss term, HNSL, whose evaluation employs several PTC 4.1procedures. HNSL is defined by the following:

HNSL≡L _(β) +L _(p) +L _(d/Fly) +L _(d/Prec) +L _(d/Ca) +L _(r) +W _(ID)/m _(AF)  (20)

HNSL bears the same numerical value for both higher or lower heatingvalue calculations, as does η_(A). Differences with PTC 4.1 and PTC 4procedures include: L_(β) is referenced to the total gross (corrected)higher heat input, (HHVP+HBC), not HHV; the L_(W) term is combined withthe ash pit term L_(p); L_(d/Fly) is sensible heat in fly ash;L_(d/Prec) is the sensible heat in stack dust at collection (the assumedelectrostatic precipitator), considered a separate stream from fly ash;and L_(d/Ca) is the sensible heat of effluents from sorbent injection ifused (e.g., CaSO₄.zH₂O and CaO effluents given limestone injection).L_(r) and W_(ID) are discussed below. All terms of Eq. (20) areevaluated relative to unity As-Fired fuel. Numerical checks of alleffluent ash is made against fuel mineral content (and optionally mayre-normalize the fuel's chemistry).

The radiation & convection factor, β_(R&C), is determined using eitherthe American Boiler Manufacturers' curve (PTC 4.1), or its equivalencemay be derived based on the work of Gerhart, Heil & Phillips (ASME,1991-JPGC-Ptc-1), or its equivalence may be based on direct measurementor judgement. The resulting L_(β) loss is always determined using thehigher heating value:

L _(β)≡β_(R&C)(HHVP+HBC)  (21A)

L_(β) is then applied to either lower or higher heating valueefficiencies through HNSL.

The coal pulverizer rejects loss term, L_(r), is referenced to the totalgross (corrected) higher heating value of rejected fuel plus the FiringCorrection, HHVP_(Rej)+HBC, given rejects contain condensed water.Further, it is assumed the grinding action may result in a concentrationof mineral matter (commonly referred to as “ash”) in the reject, thusthe fuel chemistry is renormalized based on a corrected fuel ash,α_(10-corr)=f(WF′_(Ash-AF)); see Eq. (19). This is based on the weightfraction of ash downstream from the pulverizers (true As-Fired),WF′_(Ash-AF). WF′_(Ash-AF) derives from: the weight fraction ofrejects/fuel ratio, WF_(Rej); ash in the supplied fuel, WF_(Ash-Sup);and corrected heating values. For lower heating value computations, theratio HHV_(Rej)/HHV_(Sup) in Eq. (22A) is replaced byLHV_(Rej)/LHV_(Sup).

L _(r) =WF _(Rej)(HHVP _(Rej) +HBC)  (21B)

$\begin{matrix}{{WF}_{{Ash} - {AF}}^{\prime} = {{WF}_{{Ash} - {Sup}} \cdot \frac{\begin{matrix}{\left( {1.0 - {{WF}_{Rej}{{HHV}_{Rej}/{HHV}_{Sup}}}} \right) -} \\{\left( {{WF}_{Rej}/{WF}_{{Ash} - {Sup}}} \right)\left( {1.0 - {{HHV}_{Rej}/{HHV}_{Sup}}} \right)}\end{matrix}}{\left( {1.0 - {WF}_{Rej}} \right)}}} & \text{(22A)}\end{matrix}$

The assumption of the reject loss being based on the higher heatingvalue, although convenient for the HNSL term, implies, given thepossibility of renormalized fuel chemistry, that the HRX_(Act-LHV) termmust be corrected for the fuel water's latent heat. This correction isdescribed by Eq. (22C), applied in Eq. (22B) yielding a corrected LHVP.The ΔH_(L/H) term is evaluated using As-Fired chemistry downstream fromthe pulverizers, see Eq. (39B). Within Eq. (22C):ξ≡(1.0−WF′_(Ash-AF))/(1.0−WF_(Ash-Sup)). ξ also corrects both Eq. (37B)& (39B). These same procedures are applicable for a fuel cleaningprocess where the fuel's mineral matter (ash) is removed.

LHVP=LHV+ΔH _(V/P) −ΔH _(corr−LHV)  (22B)

ΔH _(corr−LHV) =ΔH _(L/H)(ξ−1.0)/ξ  (22C)

The steam/air heater energy flow term, Q_(SAH), is assigned to HBCprovided the system encompasses this heater, which it should aspreferred. BBTC is defined in the classical manner (e.g., throttle lessfeedwater conditions, hot less cold reheat conditions). This is bestseen by equating Eqs. (13B) & (13E), noting HPR_(Act)=HPR_(Ideal)+HSL:$\begin{matrix}{{BBTC} = \quad {m_{AF}\left\lbrack {{- {HPR}_{Act}} + {HRX}_{Act} - {HNSL}} \right\rbrack}} & {\quad \text{(22D)}} \\{= \quad {m_{AF}\left\lbrack {{- \left( {{HPR}_{Ideal} + {HSL}} \right)} + \left( {{HRX}_{Cal} + {HBC}} \right) - {HNSL}} \right\rbrack}} & {\quad \text{(22E)}} \\{= \quad \left. {m_{AF}\left\lbrack {{- {HPR}_{Ideal}} + {HRX}_{Cal} + {HBC} - {HSL} - {HNSL}} \right.} \right)} & {\quad \text{(22F)}}\end{matrix}$

If Eq. (2B), and its HPR_(Ideal) term, is to be conserved, the rightside of Eq. (22F) must be corrected for the total energy flowattributable to combustion: thus HBC includes the +Q_(SAH) term, as mustthe BBTC term (resulting in a higher fuel flow). Although (BBTC−Q_(SAH))is the net “useful” output from the system, BBTC is the total anddirectly derived energy flow from the combustion process applicable toη_(B) . . . so defined such that Eqs. (13E) & (22D) are conserved. TheHSL term of Eq. (22F) is not explicitly evaluated, discussed below.

The ID fan energy flow term, W_(ID), given that thermal energy isimparted to the gas outflow stream (e.g., ID or recirculation fans), theHPR_(Act) term must be corrected (through HNSL) such that the fuel'senergy term HPR_(Ideal) is again properly conserved.

The coal pulverizer shaft power is not accounted as no thermal energy isadded to the fuel. Crushing coal increases its surface energy; for agenerally brittle material, no appreciable changes in internal energyoccur. The increased surface energy and any changes in internal energyare well accounted for through the process of determining heating value.If using ASTM D2013, coal samples are prepared by grinding to a #60sieve (250 μm). Inconsistencies would arise if the bomb calorimetersamples were prepared atypical of actual firing conditions.

Miscellaneous shaft powers are not accounted if not affecting HPR_(Act)or HRX_(Act), i.e., not affecting the energy flow attributable tocombustion. The use of “net” efficiencies or “net” heat rates,incorporating house electrical loads (the B_(Xe) term of PTC 4.1), isnot preferred for understanding the thermal performance of systems.

Having evaluated HNSL, the absorption efficiency is determined fromeither HHV- or LHV-based parameters: $\begin{matrix}{\eta_{A} = {{1.0 - \frac{HNSL}{{- {HPR}_{{Act} - {HHV}}} + {HRX}_{{Act} - {HHV}}}} = {1.0 - \frac{HNSL}{{- {HPR}_{{Act} - {LHV}}} + {HRX}_{{Act} - {LHV}}}}}} & (23)\end{matrix}$

All unburned fuel downstream of the combustion process proper (e.g.,carbon born by ash) is treated by the combustion efficiency term, as areall air, leakage and combustion water terms. For accuracyconsiderations, stack losses (HSL) are not independently computed;however to clarify, they relate for example to η_(C-HHV) as, using PTC4.1 nomenclature in Eq. (25): $\begin{matrix}{\eta_{C - {HHV}} = {1.0 - \frac{{HSL}_{HHV}}{{HHVP} + {HBC}}}} & (24)\end{matrix}$

 HSL _(HHV) =[L _(G′) +L _(mG) +L _(mF) +L _(mA) +L _(mCa) +L _(Z) +L_(H) +L _(CO) +L _(UH) +L _(UHC) +L _(UC1) +L _(UC2)]_(HHV)  (25)

where: the L_(mG) term is moisture created from combustion ofchemically-bound H/C fuel; L_(mCa) is fuel moisture bound with effluentCaSO₄; L_(UC1) is unburned carbon in fly ash; L_(UC2) is unburned carbonin bottom ash; all others per PTC 4.1. Non-combustion energy flows arenot included (see HNSL). Terms of Eq. (25) as fractions of (HHVP+HBC) or(LHVP+HBC), are computed after η_(C), by back-calculation; they arepresented only as secondary calculations for the monitoring ofindividual effects.

Combustion efficiency is determined by the following, as either HHV- orLHV-based: $\begin{matrix}{\eta_{C - {HHV}} \equiv \frac{{- {HPR}_{{Act} - {HHV}}} + {HRX}_{{Act} - {HHV}}}{{HHVP} + {HBC}}} & (26) \\{\eta_{C - {LHV}} \equiv \frac{{- {HPR}_{{Act} - {LHV}}} + {HRX}_{{Act} - {LHV}}}{{LHVP} + {HBC}}} & (27)\end{matrix}$

The development of the combustion efficiency term, as computed based onHPR_(Act) & HRX_(Act) and involving systematic use of a combustionequation, such as Eq. (19), is believed an improved approach versus theprimary use of individual “stack loss” terms. Mis-application of termsis greatly reduced. Numerical accuracy is increased. Most importantly,valid system mass and energy balances are assured.

Boiler efficiency is defined as either HHV- or LHV-based.

η_(B−HHV)=η_(C−HHV)η_(A)  (28)

η_(B−LHV)=η_(C−LHV)η_(A)  (29)

Of course fuel flow must compute identically from either efficiencybase, thus: $\begin{matrix}{m_{AF} = {\frac{BBTC}{\eta_{B - {HHV}}\left( {{HHVP} + {HBC}} \right)} = \frac{BBTC}{\eta_{B - {LHV}}\left( {{LHVP} + {HBC}} \right)}}} & (30)\end{matrix}$

Such computations of fuel flow using either efficiency, at a definedT_(Cal), is an important numerical overcheck of this invention.

After HNSL is computed, as observed in Eqs. (23), (26) & (27) only thethree major terms HPR_(Act), HRX_(Act) & HBC remain to be defined tocomplete boiler efficiency. These are defined in the followingparagraphs. To fully understand the formulations comprising HPR_(Act),HRX_(Act) & HBC, take note of the subscripts associated with theindividual terms. For example, when considering water product createdfrom combustion, n_(Comb-H2O) of Eq. (31), its Heat of Formation(saturated liquid phase) at T_(Cal) must be corrected for boundary(stack) conditions, thus, h_(Stack)−h_(f-Cal) The Enthalpies ofReactants of Eqs. (34) & (35) are determined from ideal products atT_(Cal), the Firing Correction then applied.

Differences in formulations required for higher or lower heating valuesshould also be carefully reviewed. Higher heating values require use ofthe saturated liquid enthalpy evaluated at T_(Cal); lower heating valuesrequire the use of saturated vapor at T_(Cal). Water bound with effluentCaSO₄ is assumed in the liquid state at the stack temperature; whereasits reference is the heating value base (fuel water being the assumedsource for z[H₂O] of Eq. (19)). The quantities which are not socorrected are the last two terms in Eqs. (31) & (32): water born by airand from in-leakage undergo no transformations, having non-fuel origins.Heating values and energies used in Eqs. (31) thru (35) are alwaysassociated with the system boundary: the As-Fired fuel (or the“supplied” in the case of fuel rejects), ambient air and location of theContinuous Emission Monitoring System (CEMS) and temperaturemeasurements (at the “stack”).

Enthalpy of Products (HPR_(Act))

For higher heating value calculations:

HPR _(Act−HHV) ≡ΣHPR _(i) +[n _(Comb−H2O)(ΔH _(f-Cal-liq) ⁰ +h _(Stack)−h _(f-Cal))+

 n _(Fuel−H2O)(h _(Stack) −h _(f-Cal))+n_(Lime−H2O)(h _(f-Stack) −h_(f-Cal))+

 n _(CAir−H2O)(h _(Stack) −h _(g-Cal))+n _(Leak−H2O)(h _(Stack) −h_(Steam))]_(H2O) N _(H2O)/(xN _(AF))  (31)

For lower heating value calculations:

HPR _(Act−LHV) ≡ΣHPR _(i) +[n _(Comb−H2O)(ΔH _(f-Cal/vap) ⁰ +h _(Stack)−h _(g-Cal))+

 n _(Fuel−H2O)(h _(Stack) −h _(g-Cal))+n _(Lime−H2O)(h _(f-Stack) −h_(g-Cal))+

 n _(CAir−H2O)(h _(Stack) −h _(g-Cal))+n _(Leak−H2O)(h _(Stack) −h_(Steam))]_(H2O) N _(H2O)/(xN _(AF))  (32)

where: $\begin{matrix}{{HPR}_{1} = \quad {{Enthalpy}\quad {of}\quad {non}\text{-}{water}\quad {product}\quad i\quad {at}\quad {the}\quad {boundary}}} & ~ \\{\equiv \quad {\left\lbrack {{\Delta \quad H_{f - {{Cal}/i}}^{0}} + {\int_{T_{Cal}}^{T_{Stack}}\quad {h_{i}}}} \right\rbrack n_{i}{N_{i}/\left( {xN}_{AF} \right)}}} & {\quad (33)} \\{n_{{Comb} - {H2O}} = \quad {{Molar}\quad {water}\quad {found}\quad {at}\quad {the}\quad {boundary}\quad {from}\quad {combustion}}} & ~ \\{\equiv \quad {{x\left( {{\alpha_{0}{{ZR}/2}} + \alpha_{5} + \alpha_{9}} \right)} - f}} & ~ \\{n_{{Fuel} - {H2O}} = \quad {{Molar}\quad {water}\quad {found}\quad {at}\quad {the}\quad {boundary}\quad {born}\quad {by}}} & ~ \\{\quad {{As}\text{-}{Fired}\quad {fuel}\quad \left( {{as}\quad {total}\quad {inherent}\quad {and}\quad {surface}\quad {moisture}} \right)}} & ~ \\{\equiv \quad {j_{Act} - \left\lbrack {b_{A} + b_{Z} + {\sigma \quad b_{PLS}z} + {x\left( {{\alpha_{0}{{ZR}/2}} + \alpha_{5} + \alpha_{9}} \right)} - f} \right\rbrack}} & ~ \\{n_{{Lime} - {H2O}} = \quad {{Molar}\quad {water}\quad {bound}\quad {with}\quad {effluent}\quad {CaSO}_{4}}} & ~ \\{\equiv \quad {\sigma \quad b_{PLS}z}} & ~ \\{n_{{CAir} - {H2O}} = \quad {{Molar}\quad {water}\quad {found}\quad {at}\quad {the}\quad {boundary}\quad {born}\quad {by}}} & ~ \\{\quad {{combustion}\quad {air}\quad {and}\quad {air}\quad {in}\text{-}{leakage}}} & ~ \\{\equiv \quad {b_{A}\left( {1.0 + \beta} \right)}} & ~ \\{n_{{Leak} - {H2O}} = \quad {{Molar}\quad {water}\quad {found}\quad {at}\quad {boundary}\quad {from}\quad {direct}}} & ~ \\{\quad {{in}\text{-}{leakage}}} & ~ \\{\equiv \quad b_{Z}} & ~ \\{{h_{{Stack} - {H2O}} = \quad {f\left( {P_{{stack} - {H2O}},T_{Stack}} \right)}},{{where}\quad P_{{Stack} - {H2O}}\quad {is}\quad {{water}'}s}} & ~ \\{\quad {{partial}\quad {pressure}\quad {per}\quad {wet}\quad {{molar}:}}} & ~ \\{\quad {{P_{Amb}\left( {j_{Act} + {\beta \quad b_{A}}} \right)}/{\left( {1.0 + j_{Act} + {\beta \quad b_{A}}} \right).}}} & ~\end{matrix}$

Enthalpy of Reactants (HRX_(Act))

For higher heating value calculations:

HRX_(Act−HHV) ≡HHVP+HBC+HPR _(CO2−Ideal) +HPR _(SO2−Ideal)+[(α₀ZR/2+α₅+α₉)(ΔH_(f-Cal/liq) ⁰ N)_(H2O) /N _(AF) ]+HRX _(CaCO3)  (34)

For lower heating value calculations:

HRX_(Act−LHV) ≡LHVP+HBC+HPR _(CO2−Ideal) +HPR _(SO2−Ideal)+[(α₀ZR/2+α₅+α₉)(ΔH_(f-Cal/vap) ⁰ N)_(H2O) /N _(AF) ]+HRX _(CaCO3)  (35)

where: $\begin{matrix}{{HPR}_{{CO2} - {Ideal}} = \quad {{Energy}\quad {of}\quad {CO}_{2}\quad {ideal}\quad {product}\quad {from}\quad {complete}}} \\{\quad {{combustion}\quad {at}\quad {the}\quad {calibration}\quad {{temperature}.}}} \\{\equiv \quad {\Delta \quad {H_{f - {{Cal}/{CO2}}}^{0}\left( {{\alpha_{0}{YR}} + \alpha_{4} + \alpha_{8}} \right)}N_{CO2}\text{/}N_{AF}}}\end{matrix}$ $\begin{matrix}{{HPR}_{{SO2} - {Ideal}} = \quad {{Energy}\quad {of}\quad {SO}_{2}\quad {ideal}\quad {product}\quad {from}\quad {complete}}} \\{\quad {{combustion}\quad {at}\quad {the}\quad {calibration}\quad {{temperature}.}}} \\{\equiv \quad {\Delta \quad {H_{f - {{Cal}/{SO}_{2}}}^{0}\left( {\alpha_{6} + \alpha_{9}} \right)}N_{{SO}_{2}}\text{/}N_{AF}}}\end{matrix}$ $\begin{matrix}{{HPR}_{{H2O} - {Ideal}} = \quad {{Energy}\quad {of}\quad H_{2}O\quad {ideal}\quad {product}\quad {from}\quad {complete}}} \\{\quad {{combustion}\quad {at}\quad {the}\quad {calibration}\quad {{temperature}.}}} \\{{\equiv \quad {\left( {{\alpha_{0}{ZR}\text{/}2} + \alpha_{5} + \alpha_{9}} \right)\left( {\Delta \quad H_{f - {{Cal}/{liq}}}^{0}N} \right)_{H2O}\text{/}N_{AF}}};} \\{\quad {{for}\quad {HHV}}} \\{{\equiv \quad {\left( {{\alpha_{0}{ZR}\text{/}2} + \alpha_{5} + \alpha_{9}} \right)\left( {\Delta \quad H_{f - {{Cal}/{vap}}}^{0}N} \right)_{H2O}\text{/}N_{AF}}};} \\{\quad {{for}\quad {{LHV}.}}}\end{matrix}$ $\begin{matrix}{{{HRX}_{CaCO3} = \quad {{Energy}\quad {of}\quad {injected}\quad {pure}\quad {limestone}}},{CaCO}_{3},} \\{\quad {{{at}\quad {the}\quad {calibration}\quad {temperature}};{{use}\quad {of}}}} \\{\quad {\Delta \quad H_{f - {{Cal}/{CaCO3}}}^{0}\quad {anticipates}\quad {Heats}\quad {of}\quad {Formation}}} \\{\quad {{associated}\quad {with}\quad {limestone}\quad {products}\quad {appearing}}} \\{\quad {{in}\quad {{Eq}.\quad (33).}}} \\{\equiv \quad {\Delta \quad H_{f - {{Cal}/{CaCO3}}}^{0}{b_{PLS}\left( {1.0 + \gamma} \right)}N_{CaCO3}\text{/}\left( {xN}_{AF} \right)}}\end{matrix}$

Firing Correction (HBC)

HBC≡C _(P)(T _(AF) −T _(Cal))_(Fuel)+(Q _(SAH) +W _(FD))/m _(AF)

 +[(h _(Amb) −h _(Cal))_(Air) a(1.0+β)(1.0+φ_(Act))N _(Air)

 +(h _(g-Amb) −h _(g-Cal))_(H2O) b _(A)(1.0+β)N _(H2O)

 +(h _(Steam) −h _(f-Cal))_(H2O) b _(Z) N _(H2O)

 +C_(P)(T _(Amb) −T _(Cal))_(PLS) b _(PLS)(1.0+γ)N _(CaCO3)]/(xN_(AF))  (36)

where:

h_(g−Amb−H2O)=Saturated water enthalpy at ambient dry bulb, T_(Amb).(h_(Amb)−h_(Cal))_(Air)=ΔEnthalpy of combustion dry air relative toT_(Cal).

(h_(g-Amb)−h_(g-Cal))_(H2O)=ΔEnthalpy of moisture in combustion airrelative to saturated vapor at T_(Cal).

(h_(Steam)−h_(f-Cal))_(H2O)=ΔEnthalpy of water in-leakage to systemrelative to saturated liquid at T_(Cal).

C_(P)(T_(Amb)−T_(Cal))_(PLS)=ΔEnthalpy of pure limestone relative toT_(Cal).

The above equations are dependent on common system parameters. Commonsystem parameters are defined following their respective equations, Eqs.(31) thru (36). Further, these terms are discussed in PTC 4.1 and 4, andthroughout U.S. Pat. No. 5,790,420. In addition, the BBTC term, alsocomprising common system parameters, is determined from commonlymeasured or determined working fluid mass flow rates, pressures andtemperatures (or qualities).

Miscellaneous Calculations

Several PTCs and “coal” textbooks employ simplifying assumptionsregarding the conversion of heating values. For example, a constant issometimes used to convert from a constant volume process HHV (i.e., bombcalorimeter), to a constant pressure process HHVP. The following ispreferred for completeness, for solid and liquid fuels, and is alsoapplicable for LHV:

HHVP=HHV+ΔH _(V/P)  (37A)

ΔH _(V/P) ≡RT _(Cal,Abs)(α₅/2−α₁)/(ξJN _(AF))  (37B)

where, in US Customary Units: T_(Cal,Abs) is absolute temperature(deg−R); R=1545.325 ft-lbf/mole-R; and J=778.169 ft-lbf/Btu. For gaseousfuels, the only needed correction is the compressibility factor assumingideally computed heating values:

HHVP=HHV _(Ideal) Z  (38)

Z and HHV_(Ideal) are evaluated using American Gas Associationprocedures.

To convert from a higher (gross) to a lower (net) heating value use ofEq. (39B) is exact, where Δh_(fg−Cal/H2O) is evaluated at T_(Cal). Theoxygen in the effluent water is assumed to derive from combustion air,and not fuel oxygen (thus α₃ is not included).

LHV=HHV−ΔH _(L/H)  (39A)

ΔH _(L/H) ≡Δh _(fg−Cal/H2O)(α₀ ZR/2+α₂+α₅+α₉)N _(H2O)/(ξN _(AF))  (39B)

Discussion of Flow Diagram

To more fully explain this invention FIG. 1 is presented. Box 20 of FIG.1 represents the determination of a fossil fuel's heating value, and itscorrection if needed for a constant pressure process using Eqs. (37A) &(37B). If a gaseous fuel, determination of HHVP is generally acomputation, establishing T_(Cal) by convention; in North America 60 Fis commonly used. If a solid or liquid fuel, whose heating value istested by bomb calorimeter, T_(Cal) is measured and/or otherwiseestablished as part of the testing procedure. Box 22 describes thecalculation of the HPR_(Ideal) term, comprising HPR_(CO2−Ideal),HPR_(SO2−Ideal) and HPR_(H2O|−Ideal), expressed below Eq. (35) whereassociated Heats of Formation are computed from Eq. (18) at T_(Cal). Box30 describes the computation of the Firing Correction term, HBC, usingEq. (36) as referenced to T_(Cal) Box 32 represents the calculation ofthe uncorrected Enthalpy of Reactants evaluated at T_(Cal), from Eq.(2B) requiring results from Boxes 20 and 22. Box 40 represents thecalculation of the Enthalpy of Reactants at actual firing conditionsusing Eqs. (34) or (35), requiring input from Boxes 30 and 32. Box 42represents the calculation of the Enthalpy of Products at actualboundary exit conditions (e.g., stack temperature), using Eq. (31) or(32). Box 44 represents the calculation of the non-chemistry & sensibleheat loss term, HNSL, using Eq. (20) whose procedures and individualterms are herein discussed. Box 50 represents the computation ofcombustion efficiency, using either Eq. (26) or (27), with inputs fromBoxes 20, 30, 40, and 42. Box 52 represents the computation of boilerabsorption efficiency, using either form of Eq. (23), with inputs fromBoxes 40, 42 and 44. Box 54 represents the computation of boilerefficiency, using either Eq. (28) or (29), with inputs from Boxes 50 and52.

Typical Results

The following presents typical numerical results as evaluated by theEX-FOSS computer program, commercially available from Exergetic Systems,Inc., of San Rafael, Calif. which has now been modified to employ themethods of this invention.

To illustrate the effects of mis-using calorimetric temperature Table 1presents the results of a methane-burning boiler. As observed, boilerefficiency is insensitive to slight changes in heating values providedT_(Cal) is not varied in other terms comprising η_(B). However, whenconsistently altering T_(Cal) (as its impacts HPR_(Ideal)), resultsindicate serious, and un-reasonable, error in boiler efficiency. One maynot establish a reference temperature for the fuel's chemical energy, atT_(Cal), and then not consistently apply it to other energy terms. Ifmisapplied as suggested by Table 1, errors in ri and system heat ratewill be assured. Use of Eq. (15), given η_(B) derives from Eq. (10) &(11), demands consistency in the HPR_(Act), HRX_(Act) and HBC terms; thesame system can not have a difference in its computed fuel flow.

TABLE 1 Calorimetric Temperature Effects on Boiler Efficiency ComputedHeating Efficiency Efficiency True Effect, Value for Methane at 77 F. at60 F. Δη_(B-HHV) 23867.31 at 77 F. 83.318% 82.893% −0.425% 23891.01 at60 F. 83.333% 82.908% −0.425% Difference in efficiency −0.015% −0.015%if ignoring T_(Cal) (HHV effects only)

Table 2 presents typical effects on boiler efficiency and system heatrate of mis-use of calorimetric temperatures on a variety of coal-firedpower plants. The effect of such mis-use are considered un-reasonable.These computations are based on EX-FOSS, varying only T_(Cal). Data wasobtained from actual plant conditions.

TABLE 2 Effects on Boiler Efficiency and System Heat Rate of Mis-Use ofCalorimetric Temperature True True T_(Cal) = Effect, Effect, UnitT_(Cal) = 77 F. 68 F. Δη_(B) ΔHR/HR 110 MWe CFB coal 86.086% 85.874%−0.212% +0.237% w/Limestone 300 MWe Lignite-B, 78.771% 78.426% −0.345%+0.438% Lower Heating Value 800 MWe 81.364% 81.099% −0.265% +0.335% CoalSlurry

Table 3 lists computational overchecks of higher and lower heating valuecalculations, verifying that the computed fuel flow rates of Eq. (30),are numerically identical. These simulations were selected fromInput/Loss' installed base as having unusual complexity, based on actualplant conditions. The only changes in these simulations was input of HHVor LHV, and an EX-FOSS option flag; LHV or HHV are automaticallycomputed by EX-FOSS given input of the other.

TABLE 3 EX-FOSS Calculational Overchecks (efficiencies & fuel flow,lbm/hr) HHV LHV Unit Eff. & Flow Eff. & Flow 300 MWe 59.104% 78.426%Lignite-B 1,383,259.9 1,383,260.0 800 MWe 81.097% 88.761% Coal Slurry1,104,329.4 1,104,329.7

Several modern bomb calorimetric instruments are automated to run atT_(Cal)=95F (35C). The repeatability accuracy of these instruments isbetween ±0.07% to ±0.10%. Modern bomb calorimeters use benzoic acidpowder for calibration testing. Calibration results are typicallyanalyzed using the well-known Washburn corrections (Journal of PhysicalChemistry, Volume 58, pp.152-162, 1954). Based on these procedures, NISTStandard Reference Material 39j certification for benzoic acid makes amultiplicative correction for temperature: [1.0−45.0×10⁻⁶ (T_(Cal)−25°C.)]. Such corrective coefficients (e.g., 45.0×10⁻⁶) were computed for anumber of coals, using average chemistries for different coal Ranks, andwith methane. For example, a correction of 122×10⁻⁶ implies a 0.122%change in HHV over 10° C. As observed below in Table 4, heating valueswith increasing fuel moisture are generally increasingly sensitive tocalorimetric temperature, especially for gaseous fuels and poor qualitylignite coals. Effects on HHVs associated with the common coals are notgreat. However, the sensitivity of temperature on HPR_(Ideal) isappreciable for most Ranks; computed using EX-FOSS. This sensitivitydemonstrates the fundamental cause for the sensitivities observed inTables 1 and 2.

TABLE 4 Temperature Coefficients for Meating Value Corrections andHPR_(Ideal) Temperature Sensitivity HHV Temp ΔHPR_(Ideal) Coal Fuel FuelAvg HHV Coef. HPR_(Ideal) Rank Water Ash at 25 C. (×10⁻⁶/1ΔC)(×10⁻⁶/1ΔC) an 3.55 9.85 12799.75 19.56 376.6 sa 1.44 16.51 12466.1730.10 285.0 lvb 1.74 13.24 13087.76 39.22 347.7 mvb 1.75 11.48 13371.7541.88 380.5 hvAb 2.39 10.86 13031.61 47.77 444.2 hvBb 5.61 11.8311852.63 56.53 446.7 hvCb 9.89 12.32 10720.40 60.18 450.6 subA 12.858.71 10292.89 51.16 398.3 subB 17.87 9.57 9259.75 61.15 408.0 subC 23.7910.67 8168.69 75.14 423.3 ligA 29.83 9.64 7294.66 83.56 439.4 ligB-P28.84 22.95 4751.83 122.17 481.3 ligB-G 54.04 19.30 2926.82 246.01 685.2Methane .00 .00 23867.31 105.39 424.3 Benzoic .00 .00 11372.40 45.00392.6

The method of this invention generally causes an insensitivity incomputed fuel flow when using an arbitrary reference temperature over areasonable range. Table 5 demonstrates this for several coal Ranks,assuming T_(RA) changed from 68F to 77F, and from 68F to 95F. Sucheffects on fuel flow are additive to those associated with boilerefficiency when considering net effects on system heat rate (systemefficiency).

TABLE 5 Effect of Computed Fuel Flow, Eq.(15), Given Changes toReference Temperature Effect on Fuel Flow Effect of Fuel Flow Coal Rank(T_(RA) = 68 to 77 F.) (T_(RA) = 68 to 95 F.) an +0.0051% +0.0148% hvCb−0.0251% −0.0758% subC −0.0273% −0.0824% ligB −0.1118% −0.3371%

The results illustrated in Tables 1, 2 and 4 indicate generallyun-reasonable sensitivity in computed boiler efficiency and system heatrate. Considered reasonable accuracy as attainable using the methods ofthis invention, are Δη_(B−HHV) errors, or Δη_(B−LHV) errors, in boilerefficiency of 0.15% Δη_(B) or less. Considered reasonable accuracy incomputed system heat rate are ΔHR/HR errors no greater than 0.25%.Considered reasonable accuracy in computed fuel flow, using Eq. (15),are Δm_(AF)/m_(AF) errors no greater than 0.10%.

Summary

This work demonstrates a systemic approach to determining boilerefficiency. It demonstrates that the concept of defining boilerefficiency in terms of the Enthalpy of Products (HPR_(Act)), theEnthalpy Reactants (HRX_(Act)) and the Firing Correction (HBC), it isbelieved, provides enhanced accuracy when these major boiler efficiencyterms are referenced to the same calorimetric temperature. Such accuracyis needed by the Input/Loss Method, and for the improvement of fossilcombustion in a competitive marketplace. The HPR_(Act) & HRX_(Act)concept forces an integration of combustion effluents with fuelchemistry through stoichiometrics.

What is claimed is:
 1. A method for determining a higher heating valueboiler efficiency for a thermal system which applies consistently afuel's calorimetric temperature, comprising the steps of: (a)determining a fuel's higher heating value and the associatedcalorimetric temperature; (b) equating a thermodynamic referencetemperature used to evaluate a boiler's energy flows, to thecalorimetric temperature as established when determining the fuel'shigher heating value; (c) calculating an Enthalpy of Products, anEnthalpy of Reactants and a Firing Correction as a function of thefuel's higher heating value, common system parameters, and thethermodynamic reference temperature; (d) calculating the combustionefficiency as a function of the higher heating value, the Enthalpy ofProducts, the Enthalpy of Reactants, and the Firing Correction; (e)calculating a boiler efficiency from the combustion efficiency and aboiler absorption efficiency; (f) calculating a fuel flow to the thermalsystem from the boiler efficiency, an energy delivered from thecombustion process, the fuel's higher heating value and the FiringCorrection; and (g) calculating an effluent flow output from the thermalsystem from the fuel flow and system stoichiometrics.
 2. A method fordetermining higher heating value boiler efficiency for a thermal systemwhich applies consistently any thermodynamic reference temperature,comprising the steps of: (a) determining a fuel's higher heating value;(b) using any thermodynamic reference temperature to evaluate a boiler'senergy flows, wherein a reasonable change in the thermodynamic referencetemperature does not substantially affect a computed boiler efficiencyor a computed fuel flow; (c) calculating an Enthalpy of Products, anEnthalpy of Reactants and a Firing Correction as a function of thefuel's higher heating value, common system parameters, and thethermodynamic reference temperature; (d) calculating the combustionefficiency as a function of the higher heating value, the Enthalpy ofProducts, the Enthalpy of Reactants, and the Firing Correction; (e)calculating a boiler efficiency from the combustion efficiency and aboiler absorption efficiency; (f) calculating a fuel flow to the thermalsystem from the boiler efficiency, an energy delivered from thecombustion process, the fuel's higher heating value and the FiringCorrection; and (g) calculating an effluent flow output from the thermalsystem using the fuel flow and system stoichiometrics.
 3. A method fordetermining higher heating value boiler efficiency, comprising theconcept of using a fuel's calorimetric temperature for the thermodynamicreference energy level of an Enthalpy of Products term, for thethermodynamic reference energy level of an Enthalpy of Reactants term,and also for the thermodynamic reference energy level of a FiringCorrection term evaluated independent of a fuel flow and an effluentflow, said terms comprising the major terms of a computed boilerefficiency.
 4. A method for determining a lower heating value boilerefficiency for a thermal system which applies consistently a fuel'scalorimetric temperature, comprising the steps of: (a) determining afuel's lower heating value and the associated calorimetric temperature;(b) equating a thermodynamic reference temperature used to evaluate aboiler's energy flows, to the calorimetric temperature as establishedwhen determining the fuel's lower heating value; (c) calculating anEnthalpy of Products, an Enthalpy of Reactants and a Firing Correctionas a function of the fuel's lower heating value, common systemparameters, and the thermodynamic reference temperature; (d) calculatingthe combustion efficiency as a function of the lower heating value, theEnthalpy of Products, the Enthalpy of Reactants, and the FiringCorrection; (e) calculating a boiler efficiency from the combustionefficiency and a boiler absorption efficiency; (f) calculating a fuelflow to the thermal system from the boiler efficiency, an energydelivered from the combustion process, the fuel's lower heating valueand the Firing Correction; and (g) calculating an effluent flow outputfrom the thermal system from the fuel flow and system stoichiometrics.5. A method for determining lower heating value boiler efficiency for athermal system which applies consistently any thermodynamic referencetemperature, comprising the steps of: (a) determining a fuel's lowerheating value; (b) using any thermodynamic reference temperature toevaluate a boiler's energy flows, wherein a reasonable change in thethermodynamic reference temperature does not substantially affect acomputed boiler efficiency or a computed fuel flow; (c) calculating anEnthalpy of Products, an Enthalpy of Reactants and a Firing Correctionas a function of the fuel's lower heating value, common systemparameters, and the thermodynamic reference temperature; (d) calculatingthe combustion efficiency as a function of the lower heating value, theEnthalpy of Products, the Enthalpy of Reactants, and the FiringCorrection; (e) calculating a boiler efficiency from the combustionefficiency and a boiler absorption efficiency; (f) calculating a fuelflow to the thermal system from the boiler efficiency, an energydelivered from the combustion process, the fuel's lower heating valueand the Firing Correction; and (g) calculating an effluent flow outputfrom the thermal system using the fuel flow and system stoichiometrics.6. A method for determining lower heating value boiler efficiency,comprising the concept of using a fuel's calorimetric temperature forthe thermodynamic reference energy level of an Enthalpy of Productsterm, for the thermodynamic reference energy level of an Enthalpy ofReactants term, and also for the thermodynamic reference energy level ofa Firing Correction term evaluated independent of a fuel flow and aneffluent flow, said terms comprising the major terms of a computedboiler efficiency.
 7. A method to evaluate either higher or lowerheating value efficiencies such that their computed fuel flows are notsensitive to reasonable changes in a thermodynamic reference temperatureused to determine the energy level of an Enthalpy of Products term, usedto determine the energy level of an Enthalpy of Reactants term, and alsoused to determine the energy level of a Firing Correction term evaluatedindependent of a fuel flow and an effluent flow, said terms comprisingthe major terms of a computed boiler efficiency.
 8. A method to evaluateeither higher or lower heating value efficiencies such that theircomputed fuel flows are the same, comprising the steps of: (a)determining a fuel's higher heating value; (b) calculating an Enthalpyof Products and an Enthalpy of Reactants based on the fuel's higherheating value, common system parameters and a thermodynamic referencetemperature; (c) calculating a Firing Correction based on common systemparameters and a thermodynamic reference temperature; (d) calculatingthe difference between the Enthalpy of Products and the Enthalpy ofReactants, both based on the fuels' higher heating value; (e)calculating the higher heating value combustion efficiency as a functionof the fuel's higher heating value, the difference in the Enthalpy ofProducts and the Enthalpy of Reactants as based on the fuel's higherheating value, and the Firing Correction; (f) calculating a higherheating value boiler efficiency from the higher heating value combustionefficiency and a boiler absorption efficiency; (g) determining a fuel'slower heating value; (h) calculating an Enthalpy of Products and anEnthalpy of Reactants based on the fuel's lower heating value, commonsystem parameters and a thermodynamic reference temperature; (i)calculating a Firing Correction based on common system parameters and athermodynamic reference temperature; (j) calculating the differencebetween the Enthalpy of Products and the Enthalpy of Reactants, bothbased on the fuels' lower heating value; (k) calculating the lowerheating value combustion efficiency as a function of the fuel's lowerheating value, the difference in the Enthalpy of Products and theEnthalpy of Reactants as based on the fuel's lower heating value, andthe Firing Correction; (l) calculating a lower heating value boilerefficiency from the lower heating value combustion efficiency and aboiler absorption efficiency; (m) calculating a fuel flow to the thermalsystem from either the higher heating value boiler efficiency of step(f), an energy delivered from the combustion process, the fuel's higherheating value and the Firing Correction, or from the lower heating valueboiler efficiency of step (l), an energy delivered from the combustionprocess, the fuel's lower heating value and the Firing Correction, suchthat these fuel flows are the same.
 9. A method for determining a higherheating value boiler efficiency for a thermal system which appliesconsistently a fuel's calorimetric temperature, comprising the steps of:(a) determining a fuel's higher heating value and the associatedcalorimetric temperature; (b) equating a thermodynamic referencetemperature used to determine the energy levels of the major terms ofcomputed boiler efficiency, to the calorimetric temperature asestablished when determining the fuel's higher heating value; (c)calculating an Enthalpy of Products, an Enthalpy of Reactants, and aFiring Correction as a function of the fuel's higher heating value,common system parameters, and the thermodynamic reference temperature;(d) determining a set of losses effecting computed boiler efficiency;(d) calculating a boiler efficiency as a function of the higher heatingvalue, the Enthalpy of Products, the Enthalpy of Reactants, the FiringCorrection, and the set of losses; and (e) reporting the boilerefficiency.
 10. The method of claim 9, further comprising an additionalstep, after the step of reporting, of: (f) calculating a fuel flow tothe thermal system based on the boiler efficiency, an energy flowdelivered from the combustion process, the fuel's higher heating value,and the Firing Correction.
 11. The method of claim 10, furthercomprising an additional step, after the step of calculating the fuelflow, of: (g) calculating an effluent flow output from the thermalsystem based on the fuel flow and system stoichiometrics.
 12. A methodfor determining a lower heating value boiler efficiency for a thermalsystem which applies consistently a fuel's calorimetric temperature,comprising the steps of: (a) determining a fuel's lower heating valueand the associated calorimetric temperature; (b) equating athermodynamic reference temperature used to determine the energy levelsof the major terms of computed boiler efficiency, to the calorimetrictemperature as established when determining the fuel's lower heatingvalue; (c) calculating an Enthalpy of Products, an Enthalpy ofReactants, and a Firing Correction as a function of the fuel's lowerheating value, common system parameters, and the thermodynamic referencetemperature; (d) determining a set of losses effecting computed boilerefficiency; (d) calculating a boiler efficiency as a function of thelower heating value, the Enthalpy of Products, the Enthalpy ofReactants, the Firing Correction, and the set of losses; and (e)reporting the boiler efficiency.
 13. The method of claim 12, furthercomprising an additional step, after the step of reporting, of: (f)calculating a fuel flow to the thermal system based on the boilerefficiency, an energy flow delivered from the combustion process, thefuel's lower heating value, and the Firing Correction.
 14. The method ofclaim 13, further comprising an additional step, after the step ofcalculating the fuel flow, of: (g) calculating an effluent flow outputfrom the thermal system based on the fuel flow and systemstoichiometrics.